From 1772 to 1775, during his second expedition—a fruitless bid to find the mythical Terra Australis—Captain James Cook cruised Polynesia on the H.M.S. Resolution. He stopped to chart Easter Island, the launching point for this voyage aboard the 114-passenger M.S. Caledonian Sky. The next few ports, in the Pitcairn Islands, recall another Royal Society foray some 15 years later, as the place settled by some of the mutineers of the H.M.S. Bounty. Meet some of their descendants before calling on the idyllic, if less storied, island of Mangareva and the Tuamotus archipelago for nature walks and snorkeling amid iridescent fish. Wilderness Travel: “In the Wake of the Bounty: Easter Island to Tahiti aboard the M.S. Caledonian Sky,” 19 days; $11,495; www.wildernesstravel.com

South Georgia Island: Shackleton Quest

Crammed with mountains, glaciers, and penguins, this stark place can seem more like the Antarctic than Antarctica itself, say those who’ve been to both. The Anglo-Irish polar explorer Ernest Shackleton landed here in 1916 after sailing 800 treacherous miles in an open boat, only to trudge across the island in a bid for safety. Retrace his journey, by ski and sleigh, from King Haakon Bay up the Murray Snowfield, over the spine of the Trident Ridge to Crean Glacier, and over the final hump from Fortuna Bay to the remains of the Stromness whaling station. Polar Explorers: “Shackleton Crossing of South Georgia Island,” 17 days; $18,350; www.polarexplorers.com

New Zealand: The Shire and More

Some thrill-seekers never leave the South Island, but the less trod North Island has its share of Kiwi magic, too. This multisport romp takes you mountain biking through the Whakarewarewa Forest and trekking the Tongariro Alpine Crossing. Recoup with a soak in geothermal pools and a Maori feast cooked underground with hot stones. Finally, pay homage to that most beloved of explorers, Bilbo Baggins, with a visit to the set of The Hobbit. Active New Zealand: “Kauri,” 5 days; $1,999; www.activenewzealand.com

Contributing editor Margaret Loftus has reported and written “Tours of a Lifetime” for the past eightyears.